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Optical 3D shape measurement and wear evaluation method of power head of rotary drilling rig
Optik - International Journal for Light and Electron Optics 171 (2018) 565–570
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.com/locate/ijleo
Original research article
Optical 3D shape measurement and wear evaluation method of power head of rotary drilling rig
T
⁎
Xinghua Lua, , Tao Jiangb a b
School of Mechanical and Electrical Engineering, Xuzhou University of Technology, Xuzhou 221018, China College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China
A R T IC LE I N F O
ABS TRA CT
Keywords: Shape measurement Wear evaluation Optical lattice Rotary drilling rig
Power head of rotary drilling rig is a core work unit, whose wear degree affects work intensity and efficiency. However, there are few reasonable solutions to wear detection of the power head. This paper proposes a method of measuring surface based on optical lattices and applies it to surface reconstruction of power head. In general, we project an optical lattice with a certain regularity onto an object, calculate the three-dimensional shape of surface based on lattice offset on the CCD camera, and then use polynomial fitting to calculate the expression of the surface. The evaluation of the damage degree of the surface data of the power head is converted into a two-dimensional image noise evaluation, and an evaluation model for quantifying the wear degree of the power head is established. In the experiment, we prove the high precision of the optical lattice measurement system in this work. According to the proposed evaluation model, the wear evaluation results are in line with actual ones. Further, this method can be extended to general surface measurement and wear evaluation.
1. Introduction Rotary drilling rig is a kind of engineering machinery, which is widely used in mine rock mining. Power head is the core part of the rotary drilling rig, and it is the main forces part [1]. Long-time friction between the outer surface of the power head and the hard rock is easy to cause surface damage. In order to evaluate and predict the effective working time of rotary drilling rig, we need to obtain the outer surface morphology of the power header, as well as to achieve the damaged condition [2]. Conventional wear detection method of external surface of the power head is determined manually, which is low efficiency, poor accuracy and less of quantitative data on the degree of wear. Some of broken wear detection methods are based on visual images, and degree of wear are judged by the image processing [3,4]. There are some methods for deep learning used to detect the weak condition by creating a network of evaluation and prediction with a large number of worn images. This method can get relatively accurate wear state, but it requires a large number of image samples in early stage, and the accuracy is low. Optical projection measurement is a kind of high precision, non-contact and high efficiency measurement method [5–7]. It has advantages in 3D topography measurement. By projecting light with coded information on a measured object, and capturing the image modulated by object with an industrial camera, we can solve three-dimensional information of the measured surface according to the modulation information. Phase shifting method [8–11] applied more often around projection measurement methods. It obtains topography data by solving phase. However, the phase unwrapping is affected by reflection, discontinuity, and noise of measured object, and the effect is not stable. Therefore, researchers proposed a projection-based measurement method based on optical lattice,
⁎
Corresponding author. E-mail address: [email protected] (X. Lu).
https://doi.org/10.1016/j.ijleo.2018.06.057 Received 21 April 2018; Accepted 11 June 2018 0030-4026/ © 2018 Elsevier GmbH. All rights reserved.
Optik - International Journal for Light and Electron Optics 171 (2018) 565–570
X. Lu, T. Jiang
Fig. 1. Deformation measurement model.
and carried out a large amount of research in biomedical and high-resolution microscopy imaging technology [12–14]. An optical lattice is a spatially periodic coherent pattern formed by superposition of plane waves with certain regularities. Projecting optical lattice onto object, we can solved three-dimensional shape of the object based on phase information. However, optical lattice has less application in wear detection. It is mainly because that the image information reflected by the CCD camera is different when the optical lattice is projected onto objects of different materials, and lattice processing is difficult. In this work, we propose an optical dot-matrix-based projection measurement method, and apply it to wear detection of power head of rotary drilling rigs. Firstly, we produce a usable optical lattice by adjusting and controlling the light field. Further, we establish a mathematical model for measuring the deformation variables. We solve deformation variable on the CCD directly and obtain three-dimensional shape of an object. Next, we performed faceted three-dimensional reconstruction of power head of rotary drilling rig. We give a quantitative method of the degree of wear of the power head, and evaluate the degree of wear. Experimental data show good performance of proposed method. 2. Principle and method 2.1. Optical measurement method The optical lattice-based measurement schematic is illustrated in Fig. 1. First, an optical dot pattern with a certain period generated by a computer is transmitted to an optical modulator. Then, we use two lenses to make twice Fourier transform of the emitted light and project it onto the measured object. The third step is to use a CCD camera to capture the image of an object with an optical lattice projection and calculate the corresponding deformation. System is simplified to a geometric model displayed in Fig. 2. Object is placed vertically. H2 is a point on the measured surface, and H1 is a point on the established coordinates that corresponds to H2. Angle between OH2 and x is θx . Light reflected by H1 emerges along H2B and eventually reflects towards point B2 on the CCD. At the same time, light reflected by H2 emerges along H2A and finally hits point A2 on the CCD. The optical lattice difference A2B2 formed after being modulated is the object shape variable. In Fig. 2, f1 and f2 are the focal lengths of Len 1 and Len 2, respectively. K1 and K2 are separately the magnification of illumination and imaging system. Length of OH1 is K1x. According to geometrical relationship of tiny transmission H1B = OD = f1. Thus, in Len 1 plane, we can get:
AB = H2 B tan(2θx ) =(H2 H1 + H1 B )tan(2θx ) =(f1 + K1 x tan(θx ))tan(2θx )
(1)
DC = OD tan(2θx ) = f1 tan(2θx )
(2)
Fig. 2. Equivalent mathematic model. 566
Optik - International Journal for Light and Electron Optics 171 (2018) 565–570
X. Lu, T. Jiang
Through imaging system, corresponding points B2 and A2 of H1 and H2 on the CCD have a length of A2B2, which can be expressed as it:
A2 B2 = O2 A2 − O2 B2 = A1 C1 − O1 B1 = K2 (AC − DB )
(3)
Where, AC and DB are respectively expressed by:
AC = DA − DC = AB + DB − DC
(4)
DB = OH1 = K1 x
(5)
Eq. (4) is substituted in Eqs. (1), (2) and (5), and a general expression can be obtained,
AC = (f1 + K1 x tan(θx ))tan(2θx ) + K1 x − f1 tan(2θx ) = K1 x (1 + tan(θx )tan(2θx ))
(6)
Taking Eqs. (5) and (6) into Eq. (3), A2B2 can be finally described as follow: (7)
A2 B2 = K1 K2 x tan(θx )tan(2θx ) Therefore, A2B2 is the deformation amount ΔSx of modulated optical lattice in x direction. As shown in Fig. 3, on CCD plane, the horizontal resolution of the CCD at the tilt angle θx can be calculated by:
tan(θx ) =
Δh x xc
(8)
Where, Δh x represents the CCD horizontal offset, x c represents the vertical offset. Combine Eqs. (8) and (7), we can obtain it:
A2 B2 = K1 K2 x
Δh x2 − Δh x2)
xc2 (xc2
(9)
and
xc =
xp (10)
K1
Wherein, x p indicates CCD pixel size. Similarly, if H1 is inclined by θy in y-direction, deformation variable ΔSy in y- direction can be expressed as
ΔSy = K1 K2 y tan(θy )tan(2θy )
(11)
After obtaining the x- and y-direction deformation variables of the measured object, we use a Zernike polynomial to fit measured surface. The three-dimensional shape H(x, y) of measured surface can be expressed as a Zernike polynomial with k terms. k
H (x , y ) =
∑ wi Zi (x , y)
(12)
i=1
Where wi is Zernike polynomial coefficient. Calculate partial differentials for x and y in (9) as follows: ∂H (x , y ) ∂x ⎨ ∂H (x , y) ⎩ ∂y
⎧
∂Zi (x , y ) ∂x k ∂Z (x , y ) ∑i = 1 wi i∂y k
= ∑i = 1 wi =
(13)
From the established optical measurement model, it can be seen that the deformation of n optical lattices is:
Fig. 3. Geometric enlarged view of CCD. 567
Optik - International Journal for Light and Electron Optics 171 (2018) 565–570
X. Lu, T. Jiang
⎧ ΔSx = Hx (x j , yj ) ⎨ ΔSy = Hy (x j , yj ) ⎩
(14)
Where i = 1,2,… n. So the face shape can be expressed as (15)
H = Kw
⎡ Hx (x j , yj ) ⎤ ∂Z (x , y ) ∂Z (x , y ) T Where H = ⎢ , K = ⎡ i∂x , i∂y ⎤ , w = [w1, w2, ..., wk ]T . We use nonlinear least squares method to solve the coefficient ⎣ ⎦ Hy (x j , yj ) ⎥ ⎣ ⎦ matrix w . Substitute w into Eq. (9), we can obtain three-dimensional shape of the measured surface. 2.2. Damage evaluation method The power head is cylindrical and rubs against hard rock during high-speed rotation. The long-term contact friction produces different forms of wear on the surface, and different degrees of wear correspond to changes in the micro-topography. To describe the degree of surface roughness wear reasonably, a damage evaluation model based on surface topography data was established. After obtaining the 3D data, we select a part of the 3D data for polynomial fitting. Set the area D : {(x , y ) x1 < x < x2 , y1 < y < y2 } and project this area to horizontal direction, that is, let H = 0. Infinitesimal of the surface three-dimensional data can be expressed as k ds . Its normal vector is n = (Fx , Fy , FH ) , where Fx , Fy , FH denote the partial derivatives of F = ∑i = 1 wi Zi (x , y ) − H (x , y ) in three T directions, respectively. We note that nH = (0, 0, 1) denotes the normal vector of the surface element after projection, Then, angle θ between ds and horizontal plane is
θ = arccos
nnH n nH
So the total projected area of the selected area D is S =
(16)
∬ cos θds . D
Creatively, we regard the part projected on the horizontal plane as an image I, whose width is (x2 − x1)cos θ and height is (y − y )cos θ (x − x )cos θ (y2 − y1)cos θ . We divide the image into m × n and unit size is dx = 2 m1 and dy = 2 n1 . Therefore, the next step is process the image to acquire wear information. Since the three-dimensional data is directly projected onto the plane, if the surface is rough or defective, the image will be very noisy. It is very reasonable to take the area where the noise exceeds a certain level in the image as the defect area. Here an image convolution algorithm is used for noise evaluation. We assume Laplacian image templates as follows:
1 0 1⎤ ⎡0 1 0⎤ 1⎡ L1 = ⎢ 1 −4 1 ⎥, L2 = 2 ⎢ 0 −4 0 ⎥, ⎣0 1 0⎦ ⎣1 0 2⎦ We construct J = 2(L2 − L1) . The noise description factor can be expressed as
σij =
I (i, j )*J 255
(17)
Where I (i, j ) represents grayscale value at image coordinate (i, j ) . We take a relatively smooth image and calculate its noise value as σ0 . Traversing all image points, If σij > σ0 , the number of noise points increases by one. So the noise area is S1 = Ndxdy . Therefore, the damage assessment factor λ can be determined by the ratio of the noise area S1 to the total projected area S. That is,
λ=
S1 S
(18)
3. Experimental results and discussion The deformed mirror is selected to perform the plane measurement experiment. The deformed surface has a very high flatness. In the experiment, it is determined that f = 500 mm, f1 = 200 mm, f2 = 25 mm, and the measurement surface size R = 12 mm. In the initial position, deformable mirror is reset. CCD camera captures image with optical lattice in the first positon and again after deformable mirror tilt at a certain angle in the x-direction. Image processing is performed on the images collected before and after tilting. The processing flow is as follows: (a) Perform adaptive thresholding; (b) Get the image contours of lattice images; (c) Calculate moment of contours; (d) Solve contours’ centroid coordinates; (e) Remove incomplete image contours and centroid coordinates. After image processing, centroid of lattice is extracted and marked on the original image as shown in Fig. 4(a). The coordinates of centroid point before and after tilting are plotted on an image as shown in Fig. 4(b). In Fig. 4(b), it can be seen that the tilted centroid point coordinates are shifted in x direction, but are almost constant in y direction. We project the coordinates of centroid coordinates onto a same image and calculate the amount of deformation. The entire plane is reconstructed using the proposed method. In order to verify the accuracy of the reconstruction method in this paper, an interferometer is used for comparison experiments. The reconstruction results and error comparisons are shown in Fig. 5. Reconstructed deformable mirror plane is smooth by proposed method and is relatively rough by interferometer. According to the error comparison chart, the measurement error is within ± 0.1 μm. The experimental results show that the accuracy of the 568
Optik - International Journal for Light and Electron Optics 171 (2018) 565–570
X. Lu, T. Jiang
Fig. 4. Optical lattice centroid extraction diagram. (a) Centroid making. (b) Centroid coordinates.
Fig. 5. Plane reconstruction result. Plane measurement results of (a) proposed method and (b) interferometer equipment, as well as (c) differences between them.
reconstruction results in this paper is high. What’s more, Accuracy of the method in this paper is limited by accuracy of extraction of centroid cytoplasm in lattice image. The surface topography of the power head reconstructed using this method is shown in Fig. 6(a). From the point cloud diagram, it can be seen that there are obvious cracks and broken defects in the point cloud. The reconstructed point cloud is dense. We use a triangular mesh to encapsulate the point cloud into a surface, as shown in Fig. 6(b). Four areas of the power head shape surface are selected for evaluation, and the image size is 400 × 500, as shown in Fig. 7. Fig. 7 shows that Fig. 7(a) image is extremely rough and the detection noise area is 10.08. The noise level of Fig. 7(b) is less than Fig. 7(a), (d) is almost no noise, and the image is very smooth. We chose line 200 for noise evaluation. On line 200, the chart of noise levels in the four cases is shown in Fig. 8. Statistics are shown in Table 1. Fig. 8 clearly shows that in the fourth case, the noise in the same row tends to zero and there is almost no change, while other situations have produced different variations. This is in line with the actual situation. Table 1 summarizes the noise area and damage degree parity factor in four cases, and quantifies the degree of damage. According to the proposed degree of damage model, the larger the value of the evaluation factor, the more severe the damage. 4. Conclusion This paper proposes an optical morphology measurement method based on optical lattice and applies it to the comprehensive evaluation of the surface damage degree of the power head of a rotary drilling rig. The mathematical model of optical lattice measurement and damage evaluation is given and verified by experiments. The measurement method of the optical lattice has the characteristics of high accuracy, high efficiency, and simple operation. It is suitable for surface measurement in a complex
Fig. 6. Three-dimensional reconstruction of power head surface. (a) Point Cloud Data; (b) Triangular Patch Data. 569
Optik - International Journal for Light and Electron Optics 171 (2018) 565–570
X. Lu, T. Jiang
Fig. 7. Image noise level evaluation of (a) case 1; (b) case 2; (c) case 3 and (d) case 4.
Fig. 8. Four cases noise level on line 200.
Table 1 Breakage factor in four cases.
Noise area Degree of breakage
1
2
3
4
10.02414 0.8534
3.43366 0.286
1.40631 0.11719
0.07478 0.0062
environment and has a good effect. Quantify the problem of damage evaluation, evaluate the roughness of the three-dimensional surface from the perspective of two-dimensional image noise, and make the degree of damage can be calculated. Acknowledgement This work is supported by Jiangsu prospective production-teaching-research combination innovative funds (BY2015024-01). References [1] J. Wang, Structural modeling and performance analysis of rotary circuit in directional drilling rig based on load sensing technology, Int. J. Wirel. Inf. Netw. (3) (2018) 1–10. [2] T.S. Ahn, D.H. Cho, Y.Z. Lee, Evaluation of friction force, wear volume and scuffing life of piston rings and cylinder blocks with different surface roughness for low friction diesel engine, Key Eng. Mater. 345–346 (2007) 713–716. [3] E.Z. Kordatos, D.G. Aggelis, T.E. Matikas, Monitoring mechanical damage in structural materials using complimentary NDE techniques based on thermography and acoustic emission, Compos. B Eng. 43 (6) (2012) 2676–2686. [4] L.M.P. Durão, J.M.R.S. Tavares, V.H.C.D. Albuquerque, et al., Image-based damage evaluation in drilled carbon/epoxy laminates, Euromech Solid Mechanics Conference – Esmc, (2012). [5] B. Yang, B. Lounis, F. Przybilla, et al., Large parallelization of STED nanoscopy using optical lattices, Opt. Express 22 (5) (2013) 5581–5589. [6] K. Bulut, M.N. Inci, Three-dimensional optical profilometry using a four-core optical fibre, Opt. Laser Technol. 37 (6) (2005) 463–469. [7] M. Zhong, W. Chen, X. Su, et al., Optical 3D shape measurement profilometry based on 2D S-transform filtering method, Opt. Commun. 300 (14) (2013) 129–136. [8] H. Zhang, L. Ji, S. Liu, et al., Three-dimensional shape measurement of a highly reflected, specular surface with structured light method, Appl. Opt. 51 (31) (2012) 7724–7732. [9] Z. Zhang, Y. Wang, S. Huang, et al., Three-dimensional shape measurements of specular objects using phase-measuring deflectometry, Sensors 17 (12) (2017) 2835. [10] M.H. Thekkumpurath, S. Hussain, T. Thekkumpuath, et al., 3D surface shape measurement based on fringe projection techniques, J. Neurol. Sci. 02 (1) (2013) e270. [11] X. Dai, X. Shao, L. Li, et al., Shape measurement with modified phase-shift lateral shearing interferometry illumination and radial basis function, Appl. Opt. 56 (21) (2017) 5954. [12] G.M. Brown, F. Chen, Optical methods for shape measurement, Opt. Eng. 39 (2000) 39. [13] H. Ren, J. Li, X. Gao, 3-D shape measurement of rail achieved by a novel phase measurement profilometry based on virtual reference fringe generated by image interpolation, Optik 161 (2018) 348–359 https://www.sciencedirect.com/science/article/pii/S0030402618301839. [14] J.F. Zhang, Z.Y. Wang, B. Cheng, et al., Atom cooling by partially spatially coherent lasers, Phys. Rev. A 88 (2) (2013).
570
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.com/locate/ijleo
Original research article
Optical 3D shape measurement and wear evaluation method of power head of rotary drilling rig
T
⁎
Xinghua Lua, , Tao Jiangb a b
School of Mechanical and Electrical Engineering, Xuzhou University of Technology, Xuzhou 221018, China College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China
A R T IC LE I N F O
ABS TRA CT
Keywords: Shape measurement Wear evaluation Optical lattice Rotary drilling rig
Power head of rotary drilling rig is a core work unit, whose wear degree affects work intensity and efficiency. However, there are few reasonable solutions to wear detection of the power head. This paper proposes a method of measuring surface based on optical lattices and applies it to surface reconstruction of power head. In general, we project an optical lattice with a certain regularity onto an object, calculate the three-dimensional shape of surface based on lattice offset on the CCD camera, and then use polynomial fitting to calculate the expression of the surface. The evaluation of the damage degree of the surface data of the power head is converted into a two-dimensional image noise evaluation, and an evaluation model for quantifying the wear degree of the power head is established. In the experiment, we prove the high precision of the optical lattice measurement system in this work. According to the proposed evaluation model, the wear evaluation results are in line with actual ones. Further, this method can be extended to general surface measurement and wear evaluation.
1. Introduction Rotary drilling rig is a kind of engineering machinery, which is widely used in mine rock mining. Power head is the core part of the rotary drilling rig, and it is the main forces part [1]. Long-time friction between the outer surface of the power head and the hard rock is easy to cause surface damage. In order to evaluate and predict the effective working time of rotary drilling rig, we need to obtain the outer surface morphology of the power header, as well as to achieve the damaged condition [2]. Conventional wear detection method of external surface of the power head is determined manually, which is low efficiency, poor accuracy and less of quantitative data on the degree of wear. Some of broken wear detection methods are based on visual images, and degree of wear are judged by the image processing [3,4]. There are some methods for deep learning used to detect the weak condition by creating a network of evaluation and prediction with a large number of worn images. This method can get relatively accurate wear state, but it requires a large number of image samples in early stage, and the accuracy is low. Optical projection measurement is a kind of high precision, non-contact and high efficiency measurement method [5–7]. It has advantages in 3D topography measurement. By projecting light with coded information on a measured object, and capturing the image modulated by object with an industrial camera, we can solve three-dimensional information of the measured surface according to the modulation information. Phase shifting method [8–11] applied more often around projection measurement methods. It obtains topography data by solving phase. However, the phase unwrapping is affected by reflection, discontinuity, and noise of measured object, and the effect is not stable. Therefore, researchers proposed a projection-based measurement method based on optical lattice,
⁎
Corresponding author. E-mail address: [email protected] (X. Lu).
https://doi.org/10.1016/j.ijleo.2018.06.057 Received 21 April 2018; Accepted 11 June 2018 0030-4026/ © 2018 Elsevier GmbH. All rights reserved.
Optik - International Journal for Light and Electron Optics 171 (2018) 565–570
X. Lu, T. Jiang
Fig. 1. Deformation measurement model.
and carried out a large amount of research in biomedical and high-resolution microscopy imaging technology [12–14]. An optical lattice is a spatially periodic coherent pattern formed by superposition of plane waves with certain regularities. Projecting optical lattice onto object, we can solved three-dimensional shape of the object based on phase information. However, optical lattice has less application in wear detection. It is mainly because that the image information reflected by the CCD camera is different when the optical lattice is projected onto objects of different materials, and lattice processing is difficult. In this work, we propose an optical dot-matrix-based projection measurement method, and apply it to wear detection of power head of rotary drilling rigs. Firstly, we produce a usable optical lattice by adjusting and controlling the light field. Further, we establish a mathematical model for measuring the deformation variables. We solve deformation variable on the CCD directly and obtain three-dimensional shape of an object. Next, we performed faceted three-dimensional reconstruction of power head of rotary drilling rig. We give a quantitative method of the degree of wear of the power head, and evaluate the degree of wear. Experimental data show good performance of proposed method. 2. Principle and method 2.1. Optical measurement method The optical lattice-based measurement schematic is illustrated in Fig. 1. First, an optical dot pattern with a certain period generated by a computer is transmitted to an optical modulator. Then, we use two lenses to make twice Fourier transform of the emitted light and project it onto the measured object. The third step is to use a CCD camera to capture the image of an object with an optical lattice projection and calculate the corresponding deformation. System is simplified to a geometric model displayed in Fig. 2. Object is placed vertically. H2 is a point on the measured surface, and H1 is a point on the established coordinates that corresponds to H2. Angle between OH2 and x is θx . Light reflected by H1 emerges along H2B and eventually reflects towards point B2 on the CCD. At the same time, light reflected by H2 emerges along H2A and finally hits point A2 on the CCD. The optical lattice difference A2B2 formed after being modulated is the object shape variable. In Fig. 2, f1 and f2 are the focal lengths of Len 1 and Len 2, respectively. K1 and K2 are separately the magnification of illumination and imaging system. Length of OH1 is K1x. According to geometrical relationship of tiny transmission H1B = OD = f1. Thus, in Len 1 plane, we can get:
AB = H2 B tan(2θx ) =(H2 H1 + H1 B )tan(2θx ) =(f1 + K1 x tan(θx ))tan(2θx )
(1)
DC = OD tan(2θx ) = f1 tan(2θx )
(2)
Fig. 2. Equivalent mathematic model. 566
Optik - International Journal for Light and Electron Optics 171 (2018) 565–570
X. Lu, T. Jiang
Through imaging system, corresponding points B2 and A2 of H1 and H2 on the CCD have a length of A2B2, which can be expressed as it:
A2 B2 = O2 A2 − O2 B2 = A1 C1 − O1 B1 = K2 (AC − DB )
(3)
Where, AC and DB are respectively expressed by:
AC = DA − DC = AB + DB − DC
(4)
DB = OH1 = K1 x
(5)
Eq. (4) is substituted in Eqs. (1), (2) and (5), and a general expression can be obtained,
AC = (f1 + K1 x tan(θx ))tan(2θx ) + K1 x − f1 tan(2θx ) = K1 x (1 + tan(θx )tan(2θx ))
(6)
Taking Eqs. (5) and (6) into Eq. (3), A2B2 can be finally described as follow: (7)
A2 B2 = K1 K2 x tan(θx )tan(2θx ) Therefore, A2B2 is the deformation amount ΔSx of modulated optical lattice in x direction. As shown in Fig. 3, on CCD plane, the horizontal resolution of the CCD at the tilt angle θx can be calculated by:
tan(θx ) =
Δh x xc
(8)
Where, Δh x represents the CCD horizontal offset, x c represents the vertical offset. Combine Eqs. (8) and (7), we can obtain it:
A2 B2 = K1 K2 x
Δh x2 − Δh x2)
xc2 (xc2
(9)
and
xc =
xp (10)
K1
Wherein, x p indicates CCD pixel size. Similarly, if H1 is inclined by θy in y-direction, deformation variable ΔSy in y- direction can be expressed as
ΔSy = K1 K2 y tan(θy )tan(2θy )
(11)
After obtaining the x- and y-direction deformation variables of the measured object, we use a Zernike polynomial to fit measured surface. The three-dimensional shape H(x, y) of measured surface can be expressed as a Zernike polynomial with k terms. k
H (x , y ) =
∑ wi Zi (x , y)
(12)
i=1
Where wi is Zernike polynomial coefficient. Calculate partial differentials for x and y in (9) as follows: ∂H (x , y ) ∂x ⎨ ∂H (x , y) ⎩ ∂y
⎧
∂Zi (x , y ) ∂x k ∂Z (x , y ) ∑i = 1 wi i∂y k
= ∑i = 1 wi =
(13)
From the established optical measurement model, it can be seen that the deformation of n optical lattices is:
Fig. 3. Geometric enlarged view of CCD. 567
Optik - International Journal for Light and Electron Optics 171 (2018) 565–570
X. Lu, T. Jiang
⎧ ΔSx = Hx (x j , yj ) ⎨ ΔSy = Hy (x j , yj ) ⎩
(14)
Where i = 1,2,… n. So the face shape can be expressed as (15)
H = Kw
⎡ Hx (x j , yj ) ⎤ ∂Z (x , y ) ∂Z (x , y ) T Where H = ⎢ , K = ⎡ i∂x , i∂y ⎤ , w = [w1, w2, ..., wk ]T . We use nonlinear least squares method to solve the coefficient ⎣ ⎦ Hy (x j , yj ) ⎥ ⎣ ⎦ matrix w . Substitute w into Eq. (9), we can obtain three-dimensional shape of the measured surface. 2.2. Damage evaluation method The power head is cylindrical and rubs against hard rock during high-speed rotation. The long-term contact friction produces different forms of wear on the surface, and different degrees of wear correspond to changes in the micro-topography. To describe the degree of surface roughness wear reasonably, a damage evaluation model based on surface topography data was established. After obtaining the 3D data, we select a part of the 3D data for polynomial fitting. Set the area D : {(x , y ) x1 < x < x2 , y1 < y < y2 } and project this area to horizontal direction, that is, let H = 0. Infinitesimal of the surface three-dimensional data can be expressed as k ds . Its normal vector is n = (Fx , Fy , FH ) , where Fx , Fy , FH denote the partial derivatives of F = ∑i = 1 wi Zi (x , y ) − H (x , y ) in three T directions, respectively. We note that nH = (0, 0, 1) denotes the normal vector of the surface element after projection, Then, angle θ between ds and horizontal plane is
θ = arccos
nnH n nH
So the total projected area of the selected area D is S =
(16)
∬ cos θds . D
Creatively, we regard the part projected on the horizontal plane as an image I, whose width is (x2 − x1)cos θ and height is (y − y )cos θ (x − x )cos θ (y2 − y1)cos θ . We divide the image into m × n and unit size is dx = 2 m1 and dy = 2 n1 . Therefore, the next step is process the image to acquire wear information. Since the three-dimensional data is directly projected onto the plane, if the surface is rough or defective, the image will be very noisy. It is very reasonable to take the area where the noise exceeds a certain level in the image as the defect area. Here an image convolution algorithm is used for noise evaluation. We assume Laplacian image templates as follows:
1 0 1⎤ ⎡0 1 0⎤ 1⎡ L1 = ⎢ 1 −4 1 ⎥, L2 = 2 ⎢ 0 −4 0 ⎥, ⎣0 1 0⎦ ⎣1 0 2⎦ We construct J = 2(L2 − L1) . The noise description factor can be expressed as
σij =
I (i, j )*J 255
(17)
Where I (i, j ) represents grayscale value at image coordinate (i, j ) . We take a relatively smooth image and calculate its noise value as σ0 . Traversing all image points, If σij > σ0 , the number of noise points increases by one. So the noise area is S1 = Ndxdy . Therefore, the damage assessment factor λ can be determined by the ratio of the noise area S1 to the total projected area S. That is,
λ=
S1 S
(18)
3. Experimental results and discussion The deformed mirror is selected to perform the plane measurement experiment. The deformed surface has a very high flatness. In the experiment, it is determined that f = 500 mm, f1 = 200 mm, f2 = 25 mm, and the measurement surface size R = 12 mm. In the initial position, deformable mirror is reset. CCD camera captures image with optical lattice in the first positon and again after deformable mirror tilt at a certain angle in the x-direction. Image processing is performed on the images collected before and after tilting. The processing flow is as follows: (a) Perform adaptive thresholding; (b) Get the image contours of lattice images; (c) Calculate moment of contours; (d) Solve contours’ centroid coordinates; (e) Remove incomplete image contours and centroid coordinates. After image processing, centroid of lattice is extracted and marked on the original image as shown in Fig. 4(a). The coordinates of centroid point before and after tilting are plotted on an image as shown in Fig. 4(b). In Fig. 4(b), it can be seen that the tilted centroid point coordinates are shifted in x direction, but are almost constant in y direction. We project the coordinates of centroid coordinates onto a same image and calculate the amount of deformation. The entire plane is reconstructed using the proposed method. In order to verify the accuracy of the reconstruction method in this paper, an interferometer is used for comparison experiments. The reconstruction results and error comparisons are shown in Fig. 5. Reconstructed deformable mirror plane is smooth by proposed method and is relatively rough by interferometer. According to the error comparison chart, the measurement error is within ± 0.1 μm. The experimental results show that the accuracy of the 568
Optik - International Journal for Light and Electron Optics 171 (2018) 565–570
X. Lu, T. Jiang
Fig. 4. Optical lattice centroid extraction diagram. (a) Centroid making. (b) Centroid coordinates.
Fig. 5. Plane reconstruction result. Plane measurement results of (a) proposed method and (b) interferometer equipment, as well as (c) differences between them.
reconstruction results in this paper is high. What’s more, Accuracy of the method in this paper is limited by accuracy of extraction of centroid cytoplasm in lattice image. The surface topography of the power head reconstructed using this method is shown in Fig. 6(a). From the point cloud diagram, it can be seen that there are obvious cracks and broken defects in the point cloud. The reconstructed point cloud is dense. We use a triangular mesh to encapsulate the point cloud into a surface, as shown in Fig. 6(b). Four areas of the power head shape surface are selected for evaluation, and the image size is 400 × 500, as shown in Fig. 7. Fig. 7 shows that Fig. 7(a) image is extremely rough and the detection noise area is 10.08. The noise level of Fig. 7(b) is less than Fig. 7(a), (d) is almost no noise, and the image is very smooth. We chose line 200 for noise evaluation. On line 200, the chart of noise levels in the four cases is shown in Fig. 8. Statistics are shown in Table 1. Fig. 8 clearly shows that in the fourth case, the noise in the same row tends to zero and there is almost no change, while other situations have produced different variations. This is in line with the actual situation. Table 1 summarizes the noise area and damage degree parity factor in four cases, and quantifies the degree of damage. According to the proposed degree of damage model, the larger the value of the evaluation factor, the more severe the damage. 4. Conclusion This paper proposes an optical morphology measurement method based on optical lattice and applies it to the comprehensive evaluation of the surface damage degree of the power head of a rotary drilling rig. The mathematical model of optical lattice measurement and damage evaluation is given and verified by experiments. The measurement method of the optical lattice has the characteristics of high accuracy, high efficiency, and simple operation. It is suitable for surface measurement in a complex
Fig. 6. Three-dimensional reconstruction of power head surface. (a) Point Cloud Data; (b) Triangular Patch Data. 569
Optik - International Journal for Light and Electron Optics 171 (2018) 565–570
X. Lu, T. Jiang
Fig. 7. Image noise level evaluation of (a) case 1; (b) case 2; (c) case 3 and (d) case 4.
Fig. 8. Four cases noise level on line 200.
Table 1 Breakage factor in four cases.
Noise area Degree of breakage
1
2
3
4
10.02414 0.8534
3.43366 0.286
1.40631 0.11719
0.07478 0.0062
environment and has a good effect. Quantify the problem of damage evaluation, evaluate the roughness of the three-dimensional surface from the perspective of two-dimensional image noise, and make the degree of damage can be calculated. Acknowledgement This work is supported by Jiangsu prospective production-teaching-research combination innovative funds (BY2015024-01). References [1] J. Wang, Structural modeling and performance analysis of rotary circuit in directional drilling rig based on load sensing technology, Int. J. Wirel. Inf. Netw. (3) (2018) 1–10. [2] T.S. Ahn, D.H. Cho, Y.Z. Lee, Evaluation of friction force, wear volume and scuffing life of piston rings and cylinder blocks with different surface roughness for low friction diesel engine, Key Eng. Mater. 345–346 (2007) 713–716. [3] E.Z. Kordatos, D.G. Aggelis, T.E. Matikas, Monitoring mechanical damage in structural materials using complimentary NDE techniques based on thermography and acoustic emission, Compos. B Eng. 43 (6) (2012) 2676–2686. [4] L.M.P. Durão, J.M.R.S. Tavares, V.H.C.D. Albuquerque, et al., Image-based damage evaluation in drilled carbon/epoxy laminates, Euromech Solid Mechanics Conference – Esmc, (2012). [5] B. Yang, B. Lounis, F. Przybilla, et al., Large parallelization of STED nanoscopy using optical lattices, Opt. Express 22 (5) (2013) 5581–5589. [6] K. Bulut, M.N. Inci, Three-dimensional optical profilometry using a four-core optical fibre, Opt. Laser Technol. 37 (6) (2005) 463–469. [7] M. Zhong, W. Chen, X. Su, et al., Optical 3D shape measurement profilometry based on 2D S-transform filtering method, Opt. Commun. 300 (14) (2013) 129–136. [8] H. Zhang, L. Ji, S. Liu, et al., Three-dimensional shape measurement of a highly reflected, specular surface with structured light method, Appl. Opt. 51 (31) (2012) 7724–7732. [9] Z. Zhang, Y. Wang, S. Huang, et al., Three-dimensional shape measurements of specular objects using phase-measuring deflectometry, Sensors 17 (12) (2017) 2835. [10] M.H. Thekkumpurath, S. Hussain, T. Thekkumpuath, et al., 3D surface shape measurement based on fringe projection techniques, J. Neurol. Sci. 02 (1) (2013) e270. [11] X. Dai, X. Shao, L. Li, et al., Shape measurement with modified phase-shift lateral shearing interferometry illumination and radial basis function, Appl. Opt. 56 (21) (2017) 5954. [12] G.M. Brown, F. Chen, Optical methods for shape measurement, Opt. Eng. 39 (2000) 39. [13] H. Ren, J. Li, X. Gao, 3-D shape measurement of rail achieved by a novel phase measurement profilometry based on virtual reference fringe generated by image interpolation, Optik 161 (2018) 348–359 https://www.sciencedirect.com/science/article/pii/S0030402618301839. [14] J.F. Zhang, Z.Y. Wang, B. Cheng, et al., Atom cooling by partially spatially coherent lasers, Phys. Rev. A 88 (2) (2013).
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